Journal of Engineering Science and Technology Vol. 11, No. 9 (2016) 1282 - 1295 © School of Engineering, Taylor’s University
1282
ADAPTATION OF JOHNSON SEQUENCING ALGORITHM FOR JOB SCHEDULING TO MINIMISE THE AVERAGE WAITING
TIME IN CLOUD COMPUTING ENVIRONMENT
SOUVIK PAL*, PRASANT KUMAR PATTNAIK
School of Computer Engineering, KIIT University, Campus 15, Bhubaneswar, India
*Corresponding Author: [email protected]
Abstract
Cloud computing is an emerging paradigm of Internet-centric business
computing where Cloud Service Providers (CSPs) are providing services to the
customer according to their needs. The key perception behind cloud computing
is on-demand sharing of resources available in the resource pool provided by
CSP, which implies new emerging business model. The resources are
provisioned when jobs arrive. The job scheduling and minimization of waiting
time are the challenging issue in cloud computing. When a large number of jobs
are requested, they have to wait for getting allocated to the servers which in turn
may increase the queue length and also waiting time. This paper includes
system design for implementation which is concerned with Johnson Scheduling
Algorithm that provides the optimal sequence. With that sequence, service
times can be obtained. The waiting time and queue length can be reduced using
queuing model with multi-server and finite capacity which improves the job
scheduling model.
Keywords: Cloud broker, Cloud computing, Queuing model, Job scheduling.
1. Introduction
Cloud computing is a service-oriented model, which is associated with academic
research and IT Industry. In cloud computing environment, computing machines
are to be built from physically distributed components such as processing
elements, data storage and software resources [1]. A cloud infrastructure can be
structured into services in agreement with the requirement of the client, which can
grow or shrink in real-time scenario [2, 3].
The end users use the computing and physical resources in utility manner which
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Journal of Engineering Science and Technology September 2016, Vol. 11(9)
Nomenclatures
c The number of servers
E[τ] Average or mean Inter-arrival time, ns
E(S) Average or mean service time, ns
K Maximum capacity of the system
Lq Average number of customers in the queue
Ls Average number of customers in the system
P(x) Probability of x arrivals; x=0,1,2,......
Wq Average waiting time in the queue, ns
Ws Average waiting time in the system, ns
x Number of arrivals per unit of time
Greek Symbols
n Average arrival rate, n=0, 1, 2,…, K-1, λn = λ; n ≥ K, λn = 0.
Average service rate
is denoted as = /c
is denoted as
0
)1(n
Knn PP
Inter-arrival time, ns
Abbreviations
CSP Cloud Service Provider
SC Service Centre
SLA Service Level Agreement
describes a business framework for delivering the services and computing power
on-demand. After getting the services, cloud users have to pay the service
providers based on their usage. This situation leads to a business relationship
through Cloud Brokerage Services which act as mediator who facilitates the users
to choose the best resources.
Cloud broker enforces easy access to cloud services from the service
providers. Through the Cloud Broker, the clients can easily get the services and
deploy the applications onto cloud platform. Cloud Broker provides a platform
whereby he collects the information from the user, analyse the data, send the data
to the CSP on behalf of the user and also provides the billing services. Cloud
Broker provides data integration services across all the components of the cloud
services. Cloud brokers are there to assist the users to keep the track of all the
activities such as execution time of each request, specific data centre used,
numbers of data centres, calculation of waiting time of each request. The user-
requests can be scheduled using Johnson Scheduling algorithm and the waiting
time can be reduced by using Queuing theory. Cloud Brokers are responsible for
implementing these algorithms which may facilitates the users as well as the
CSPs. This paper emphasizes on solving the issue of job scheduling in cloud
computing environment by Johnson algorithm. Moreover, a system design has
been modelled to fit Johnson sequencing algorithm and to minimize the waiting
time queuing theory has been used. The paper is organized as follows:
In Section 2, we have discussed modelling on service job scheduling in cloud
computing environment which illustrates the system design, state diagram of the
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design, system flow, and queuing model. In Section 3, we have presented the
numerical analysis and comparison study. Section 4 concludes the work and lastly
an Appendix A has been appended to this article.
1.1. Literature survey of the related work
Job Scheduling problem is a core research issue in the field of cloud computing
[4]. It is concerned with minimization of the waiting time after using the
scheduling algorithms. Job scheduling enhances the functioning of cloud to gain
the maximum profit. The aim of using different scheduling algorithms is to find a
proper list in which the tasks are scheduled to execute and reduce the total job
execution time. There are diverse types of scheduling algorithms presented in the
cloud environment that varies from the traditional scheduling algorithms which
may not apply to the cloud systems since cloud is a distributed environment that
comprises of heterogeneous systems.
Cloud computing, as market-oriented service utilities begun with task
scheduling concept accordingly. Some of the basic scheduling algorithms can be
used for scheduling in cloud computing, such as First Come First Serve (FCFS)
Algorithm (in the queue the job comes first, is served first) [4, 5]. As well as Round
Robin (RR) Algorithm (the jobs are being looped using a specific time slice or time
quantum until they completes their execution) [6 - 8]. There are some other
algorithms [9] like Resource-Aware-Scheduling Algorithm (RASA) [10], Reliable
Scheduling Distributed in Cloud Computing (RSDC) [11], Priority-based Service
Scheduling Policy [12] and Extended Max-Min Scheduling [13], as well as
Optimistic Differentiated Job Scheduling algorithm [14]. In the next section we will
present some of the related work on cloud computing scheduling methods.
Cepek et al. [15] have discussed non-pre emptive flow shop scheduling
whereby a set of jobs are processed through a set of service machines with some
distinct order. This is used for minimizing the makespan which in turn speed up
the performance of the system. However, Johnson Sequencing Rule (Flow Shop
Algorithm) with N Jobs and 2 Machines was proposed to find the optimal
sequence. Johnson [16] has been applied in various aspects of operational
research [17], Industry and computer applications [18, 19]. This rule finds an
optimum schedule with minimized makespan.
Buyya et al. [20] have presented cloud computing as delivering IT services
which facilitates the user with the computing utilities. Their paper deals with user-
driven service control and computational capabilities. The resources are allocated
in accordance with Service Level Agreement (SLA). Moreover, the paper also
deals with how Virtual Machines (VMs) are working according to the tasks
requested by the customers.
Jiang and Ni [21] have presented FCFS algorithm combined with backfilling
and priority strategy for task scheduling in grid computing environment. This
concept has been used for reducing the response time and also for improving the
system resource utilization. They have also considered the concept of resource
recycling after completion of all tasks.
Li [22] has focused on the resources utilization to gain the highest job
scheduling system performance. For that he has considered M/G/1 queuing model
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with non-pre-emptive priority. Their paper shows the system cost function to get
the estimated optimistic value of service designed for each job, which guarantees
Quality of Service (QoS) conditions of customer jobs and the optimal profits for
the service providers.
Sowjanya et al. [23] have discussed the queue length and waiting time. They
have applied M/M/s queuing model to reduce the mean queue length and waiting
time by varying the number of servers.
Khazaei et al. [24] have described novel estimated methodical model which
deals with performance evaluation of the servers. Their paper is meant to get the
approximation of the total probability distribution of the response time of the
requests. Their model allows the cloud providers to establish the relationship
between input buffer size and the number of Service Centres (SCs). They have
analyzed immediate service probability, blocking probability, and the average
number of tasks in the system.
Pal and Pattnaik [25] have discussed on the classification of virtualization
environment in cloud. The virtualization in cloud computing includes automatic
resources provisioning, scheduling of user request, accounting of renewal request
and so on. Virtualization can be implemented through cloud broker. Cloud broker
[26] acts as an interface to facilitate the IT user to choose the appropriate data
centre capable of providing adequate resources according to the requirement of
the customer. It is also responsible for scheduling of the tasks requested by the
customer. They have discussed on the design aspect of the cloud broker and work
flow strategy using sequence diagram. They have also shown the procedures how
the scheduling can be enabled in cloud broker.
Spicuglia et al. [27] have shown the procedures of collecting data from
different data centres in heterogeneous systems. They have discussed about how
to join the best queue and plug and play workload controller which tries to
minimize the variance and upper percentile of response times.
Guo et al. [28] have described dynamic performance optimisation in cloud
environments using M/M/S Queuing system. They have proposed the function,
strategy and synthesis optimisation mode using the queuing model. As well as
they have compared and analyzed the Shortest Service Time First and FCFS
methods which shows optimised results of average queue length, average waiting
time and the number of customers.
1.2. Objective of the study
In the previous section, we have discussed the FCFS algorithm, Johnson
Sequencing algorithm, queuing model with multi-server and finite capacity in the
system. In this paper, a system model has been designed where Johnson
Algorithm and queuing system has been implemented to minimize the service
time in cloud computing environment. Considering a batch comprising of certain
number of jobs, this is easy to find service time using Gantt chart. So that, the
service times for each job can be obtained using that Gantt chart. After that, using
the M/M/c/K queuing system it can be reduced the average number of customers
in the queue and in the system and as well as the average waiting time in the
system and in the queue.
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2. Modelling On Job Scheduling in Cloud Computing Environment
In cloud computing environment, different types of user-specific jobs are
requested. Those jobs are required to be scheduled to get the optimal sequence
which can be used to reduce the waiting time using existing queuing model.
2.1. System design
This section illustrates the aspects of system design using a schematic diagram
which deals with the scheduling phase and the queuing model. In scheduling
phase, Johnson Sequencing Algorithm has been considered to provide an
optimised sequence of jobs. As a queuing system, M/M/c/K model has been taken
to find different waiting times.
In our design as shown in Fig. 1, there are n numbers of customers who make
the request to the cloud broker. The requests can be Resource-based,
Infrastructure-based, Platform-based, Software-based or Storage-based. Cloud
broker, as an intermediation service, does identity and access management
capabilities. After authorization of the customer-access, in accordance with the
SLA service, all the requirements and user data are reported to the service
provider. The Monitor module gathers all the requests or jobs and resource
information from the user for a particular time span. The Analyser module
determines the available resources. If the requested resources are available, the
resources are provisioned according to the SLA service terms and conditions.
After getting the resource confirmation, Scheduler module schedules the jobs
according to Johnson Algorithm, which finds optimum sequence and minimize
makespan which in turn reduce the waiting time of the customers. These
scheduled jobs are passed through M/M/c/K Queuing System that leads to finding
different waiting lines which will be discussed later. Efficient usage of servers can
maximize the sharing of systems and computational resources beside minimizing
the cost complexity, and reducing the waiting time.
Fig. 1. System design.
2.2. State diagram
This section deals with the state diagram of the system design as shown in Fig. 2.
Cloud user first interacts with the cloud broker and sends User_Request ( ) in
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order to get access to the cloud infrastructure. All the information and requests are
sent using Send_Info( ) and send_request ( ).
Fig. 2. State diagram.
At that stage, for the existing customers, Renewal_Request ( ) can be executed,
for which an existing service can be renewed in accordance with the requirements
of the user. All the requests should meet the SLA. The service requested by the user
can be processed only after analyzing the available resources using
Available_Resources ( ) and Analyze_Resource_Status ( ). The resources can be
provisioned according to user’s needs. If the requested resources are not available,
the request can be thrown out by Reject_Request ( ). At that stage, the resources can
be reallocated for the existing customers by ReAllocation ( ). Then the requests are
in ready state and prepared to be executed and the requests are to be scheduled
using Schedule_Request ( ). After scheduling, they are in a queue and exit the
system after making Execute_Request ( ) and Exit ( ) respectively. In that design,
the scheduling concept and queuing concept are mainly focused to minimize the
waiting time in the system as well as in the queue.
2.3. System flow
This section deals with the system flow that is concerned with Johnson Sequencing
Algorithm followed by queuing system with finite capacity and multiple SCs. For
implementing Johnson Algorithm it has been considered the followings [16]:
Consideration 1: N jobs or requests will be executed on two SCs (SC1and SC2)
arranged in the sequential manner 21 SCSC .
Consideration 2: No SCs can process more than one job at a time.
Consideration 3: Each job, once started, must be performed till completion.
Consideration 4: All the jobs are in ready state, so that any one of them can be
picked up for processing.
Consideration 5: Time for transfer of a job from one SC to another is negligible.
In our system design, 5 numbers of jobs and the processing time of each job
are to be put in a matrix shown in Table 1. Here T[i][j] is the dimension of the
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processing time matrix, where i and j are positive integer numbers and for Table
1, i=5 and j=2.
Table 1. Processing time matrix.
Task Processing
time on SC1
Processing
time on SC2
Job 1 T11 T12
Job 2 T21 T22
Job 3 T31 T32
Job 4 T41 T42
Job 5 T51 T52
After getting this matrix, Johnson Sequencing Algorithm is implied to get the
optimised sequence and there after M/M/c/K queuing model is applied to get the
waiting lines as shown in Fig. 3.
Fig. 3. Flow Chart of the system design.
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2.4. Queuing model for cloud computing environment
Queuing theory is the learning of the phenomenon of the waiting line. The basic
queuing process is completely described by specifying [29, 30] arrival process,
service process, no of servers and the places of maximum capacity. Assuming that
user requests come to the server at a certain rate with a Poisson distribution,
whereas the process time for each job is supposed to be taken as exponential
distribution. Considering two SCs and five places of waiting positions as
capacity, it can be constructed an M/M/c/K queuing model with non-pre emptive
systems. In this paper, we have merged job shop scheduling [31] with the queuing
model. As per Kendal’s notation [32], In case of Arrival Distribution (M), Inter-
arrival times are Independent, Identically Distributed (IID) random variables with
exponential distribution. In Service Distribution (M), Service times are IID and
exponentially distributed.
Poisson fashion is considered as arrival pattern since arrivals of customers are
based on a massive numbers of independent sources. It has been taken into
consideration that page hit occurs at a certain time point zero. For modelling this
distribution we need an approximate value of λ (λ= the rate parameter). Assuming
that τ is the time between two successive arrivals. So that we assume τ = Inter-
arrival time. We can denote E[τ] as the average or mean Inter-arrival time.
Average arrival rate][
1
E .
An exponential distribution with the rate parameter λ has density a(t) = λe-λt
(t
= time of customer arrival). For any given arrival time, a Poisson distribution can
be established by using this formula:
... 2, 1, 0, = for ,!
xx
eP(x)
x
where P(x) = Probability of x arrivals, x = number of arrivals per unit of time, and
λ = Average arrival rate.
Service time is the time elapsed between the starting of the service to its
completion. In case of service process, we assumed that Service times are IID and
exponentially distributed. We assume Si be the service time of ith
customer. So
average or mean service time, denoted by E(i), will be
n
Si
SE
n
i
0)( (n = number of jobs). So that service rate will be
)(
1
SE .
In order to enable system stability, the system will be in an equilibrium
condition provided that the utilization factor 1
.
3. Numerical Analysis
This section deals with the numerical analysis and results. Assuming that there
are 5 jobs and the respective processing time of each job has been taken in a
matrix as follows:
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According to the service times in Table 2, the Gantt chart (FCFS basis) has
been made in accordance with the considerations shown in Fig. 4.
Table 2. Initial processing values.
Task Processing
time on SC1
Processing
time on SC2
Job 1 0.05 0.02
Job 2 0.01 0.06
Job 3 0.09 0.07
Job 4 0.03 0.08
Job 5 0.10 0.04
Fig. 4. Gantt chart using FCFS algorithm.
Now the service time of each process can be found using Gantt chart, and the
mean service time and the average service rate may easily be calculated.
For Job 1: service time is (0.07-0) = 0.07,
Job 2: (0.13-0.05) = 0.08,
Job 3: (0.22-0.06) = 0.16,
Job 4: (0.3-0.15) = 0.15,
Job 5: (0.34-0.18) = 0.16.
Mean service time is 5
62.0 = 0.124. and Service rate will be
)(
1
SE = 8.0645.
While considering the Johnson Sequencing algorithm, the average service rate
can be easily calculated accordingly as shown in Fig. 5.
For Job 1: service time is (0.3-0.23) = 0.07,
Job 2: (0.07-0.0) = 0.07,
Job 3: (0.22-0.04) = 0.18,
Job 4: (0.15-0.1) = 0.14,
Job 5: (0.27-0.13) = 0.14.
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Journal of Engineering Science and Technology September 2016, Vol. 11(9)
Mean service time is 5
60.0 = 0.12 and Service rate will be
)(
1
SE = 8.3333.
The results are shown in Tables 3 and 4 and the respective formulae have been
appended in Appendix A. These results show that service time and average
waiting time can be minimized by implementing Johnson Sequencing Algorithm
and queuing system in comparison to existing FCFS Algorithm in cloud
computing environment.
According to the numerical results we have discussed the comparison study
regarding Lq, Ls, Wq, and Ws. Figures 6 to 9 show that the average number of
customers and the average waiting time in the queue and in the system can be
minimized using Johnson sequencing algorithm rather than FCFS algorithm.
These comparisons produce better outcomes in case of average number of
customers and the average waiting time in case of Johnson Sequencing
Algorithm. This study helps the CSPs to provide better quality of service as
waiting time is less and leads to customer satisfaction.
Fig. 5. Gantt chart using Johnson sequencing algorithm.
Table 3. Results with FCFS algorithm.
Johnson Algorithm
Lq Ls Wq Ws
λ = 2 0.0035 0.2435 0.0017 0.1217
λ = 4 0.0280 0.5075 0.0070 0.1270
λ = 7 0.1445 0.9755 0.0209 0.1409
Table 4. Results with Johnson sequencing algorithm.
FCFS Algorithm
Lq Ls Wq Ws
λ = 2 0.0038 0.2518 0.0019 0.1259
λ = 4 0.03090 0.5263 0.0077 0.1317
λ = 7 0.1585 1.0158 0.0229 0.1469
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Journal of Engineering Science and Technology September 2016, Vol. 11(9)
Fig. 6. Analysis of the Average number
of customer in the queue (Lq).
Fig. 7. Analysis of the average number
of customer in the system (Ls).
Fig. 8. Analysis of the average
waiting time in the queue (Wq).
Fig. 9. Analysis of the average
waiting time in the system (Ws).
4. Conclusion
In recent days, cloud computing is a very popular word in academia and in
research. Cloud broker uses the virtualized computing resources and allocate them
according to the requirement of the user based on SLA policies. In this paper, we
have discussed the scheduling algorithms and queuing model with multi-server
and finite capacity. We have presented that the Johnson Algorithm and queuing
model can easily be used in suitable environment; so that it will produce better
outcomes in waiting times in comparison to FCFS with same queuing model. We
have shown in this article that using Johnson Sequencing Algorithm, an optimal
sequence can be obtained and also using M/M/c/K queuing model, the waiting
time and queue length can be reduced. We have also shown the comparison study.
At the end of this work, the related cost per service, waiting time due to increased
number of servers has been kept as the future work.
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Appendix A
Waiting Lines Formulae using M/M/c/K Queuing Model
In this article, a queuing system has been used with multiple servers and
maximum capacity denoted as M/M/c/K Model. c indentifies the number of
servers. Sometimes the systems have a finite capacity of queue. In the system
model, only maximum of K number of customers are permitted. So K is
maximum capacity of the system. Therefore, (K-c) is the queue capacity.
If the queuing system is “full”, the customers that arrive to the system are
declined to enter into the system. That means at that time the average arrival time
becomes zero. If n denotes the number of arriving customers. So we can write:
For n=0, 1, 2,…, K-1, λn = λ; and for n ≥ K, λn = 0;
For steady-state probabilities are Pn = XnP0; where
For ;,...,2 ,1 cn ;!
)/(
nX
n
n
For Kccn ,.....1, , ;!
)/(cn
n
ncc
X
For ;Kn .0nX
So that we can write,
For ;,...,2,1 cn ;!
)/(0P
nP
n
n
For ;,.....1, Kccn ;!
)/(0P
ccP
cn
n
n
For ;Kn .0nP
where .!
)/(
!
)/(1
0 10
c
n
K
cn
cncn
ccnP
It has been denoted average number of customers in the system, average
number of customers in the queue, average waiting time in the system, and
average waiting time in the queue as Ls, Lq, Ws, and Wq respectively.
.)1()(1)1(!
)/(2
0
cKcK
c
cKc
PLq
1
0
1
0
1c
n
c
Nnn PcLqnPLs , where .
c
LsWs , where
0
).1(n
Knn PP
.
LqWq